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Winner of the 2009 Japan Statistical Association Publication Prize. The Akaike information criterion (AIC) derived as an estimator of the Kullback-Leibler information discrepancy provides a useful tool for evaluating statistical models, and numerous successful applications of the AIC have been reported in various fields of natural sciences, social sciences and engineering. One of the main objectives of this book is to provide comprehensive explanations of the concepts and derivations of the AIC and related criteria, including Schwarz’s Bayesian information criterion (BIC), together with a wide range of practical examples of model selection and evaluation criteria. A secondary objective is to provide a theoretical basis for the analysis and extension of information criteria via a statistical functional approach. A generalized information criterion (GIC) and a bootstrap information criterion are presented, which provide unified tools for modeling and model evaluation for a diverse range of models, including various types of nonlinear models and model estimation procedures such as robust estimation, the maximum penalized likelihood method and a Bayesian approach. Sadanori Konishi is Professor of Faculty of Mathematics at Kyushu University. His primary research interests are in multivariate analysis, statistical learning, pattern recognition and nonlinear statistical modeling. He is the editor of the Bulletin of Informatics and Cybernetics and is co-author of several Japanese books. He was awarded the Japan Statistical Society Prize in 2004 and is a Fellow of the American Statistical Association. Genshiro Kitagawa is Director-General of the Institute of Statistical Mathematics and Professor of Statistical Science at the Graduate University for Advanced Study. His primary interests are in time series analysis, non-Gaussian nonlinear filtering and statistical modeling. He is the executive editor of the Annals of the Institute of Statistical Mathematics, co-author of Smoothness Priors Analysis of Time Series, Akaike Information Criterion Statistics, and several Japanese books. He was awarded the Japan Statistical Society Prize in 1997 and Ishikawa Prize in 1999, and is a Fellow of the American Statistical Association.

Stochastic analysis. --- Information modeling. --- Mathematical analysis. --- 517.1 Mathematical analysis --- Mathematical analysis --- Modeling, Information --- System analysis --- Analysis, Stochastic --- Stochastic processes

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Fluctuating parameters appear in a variety of physical systems and phenomena. They typically come either as random forces/sources, or advecting velocities, or media (material) parameters, like refraction index, conductivity, diffusivity, etc. The well known example of Brownian particle suspended in fluid and subjected to random molecular bombardment laid the foundation for modern stochastic calculus and statistical physics. Other important examples include turbulent transport and diffusion of particle-tracers (pollutants), or continuous densities (''oil slicks''), wave propagation and scatteri

Statistical physics. --- Stochastic analysis. --- Stochastic processes. --- Random processes --- Physics --- Analysis, Stochastic --- Statistical methods --- Probabilities --- Mathematical statistics --- Mathematical analysis --- Stochastic processes

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Stochastic analysis, a branch of probability theory stemming from the theory of stochastic differential equations, is becoming increasingly important in connection with partial differential equations, non-linear functional analysis, control theory and statistical mechanics.

Stochastic processes --- Shape theory (Topology) --- Mathematics --- Physical Sciences & Mathematics --- Geometry --- Homotopy theory --- Mappings (Mathematics) --- Topological manifolds --- Topological spaces --- Stochastic analysis. --- Analysis, Stochastic --- Mathematical analysis

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Stochastic analysis.. --- Anàlisi estocàstica --- Analysis, Stochastic --- Mathematical analysis --- Stochastic processes --- Anàlisi matemàtica --- Processos estocàstics --- Càlcul de Malliavin --- Equacions integrals estocàstiques --- Integrals estocàstiques

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Stochastic processes --- Brownian motion processes. --- Stochastic analysis. --- Mouvement brownien, Processus de --- Analyse stochastique --- 51 <082.1> --- Mathematics--Series --- Brownian motion processes --- Stochastic analysis --- Analysis, Stochastic --- Mathematical analysis --- Wiener processes --- Brownian movements --- Fluctuations (Physics) --- Markov processes